What problem does it solve? Implementing QSP-based Hamiltonian simulation requires correctly combining block encoding, Bessel-derived Chebyshev coefficients, LCU circuit construction, and time-slice management, which is error-prone without a structured reference. ## Core Features & Use Cases - QSP-HS Algorithm Guide: Explains how QSPHSAlgorithm approximates e^{-iHt} by block-encoding a Hamiltonian and applying polynomial spectral transformations, with full parameter and return-value documentation. - Accuracy vs. Depth Control: Details how degree, beta, and automatic time_slices expansion jointly control approximation error and circuit depth, including the degree estimation formula. - Reference Implementations: Provides a verification script and a manual matrix-level implementation for debugging, validation, and reimplementation. - Use Case: A researcher benchmarking Hamiltonian simulation methods can run parameter sweeps over evolution time and polynomial degree, then compare the Frobenius-norm error against exact scipy.linalg.expm results. ## Quick Start Ask the assistant to run QSP Hamiltonian simulation on the 2x2 Hermitian matrix [[2,1],[1,3]] with t=1.0, error=1e-8, degree=15, and report the Frobenius-norm error.
